The Viscosity and Self-Diffusion of Some Real Colloidal Ferrofluids
Round 1
Reviewer 1 Report
Comments for author File: 
Comments.pdf
Author Response
Response to Reviewer 1 Comments
Thank you very much for your valuable comments regarding our manuscript.
In this letter, we would like to explain our revisions.
Point 1: The main findings should be included in the abstract.
Response 1: This is done in the abstract of the new manuscript version
Point 2: Method solution is expected to be specified in the abstract.
Response 2: This is done in the abstract of the new manuscript version
Point 3: The aim and objectives of the study is not specified, kindly include these.
Response 3: This is done in the abstract and section 1 of the Introduction of the new manuscript version
Point 4: The significance and motivation of the study are not clear; the authors should clarify these.
Response 4: This is done in the introduction section 1 of the new manuscript.
Point 5: The initial and boundary conditions of the governing model
must be clearly stated.
Response 5: In lines 176 and 177 of the new version of the manuscript appear now stated the boundary conditions that the fitting of the experimental structure factor S(k) with RMSA theory must satisfy the boundary condition of minimum error of their differences. Also, the associated pair correlation function at contact must be zero, that is to say;
This boundary condition is also stated in line 389 of Appendix B. Further in line 400 of Appendix C, To evaluate numerically the integral of Eq. (1), the initial condition =1 is used.
Point 6: You need to describe the method of solution in detail and the application procedures.
Response 6: To answer this query, we made the three new Appendices, A, B, and C, that provided detailed information on all methods of solution used to determine the structure factor S(k) fitting to
the experimental data. Its use in calculating de diffusion coefficient and the viscosity
Point 7: The authors should explain what prompted the choice of method of solution used over other
techniques.
Response 7: As we stated in Section 1 of Introduction, line 91: The RMSA theory demonstrated that it could accurately reproduce the experimental stricture factor of a fluid made of particles with Yukawa repulsive interaction. These facts can be verified in figures 1(a), 3, 5, and 6. On the other hand, as stated in line 298 of section 3 of Results and discussion, from low up to moderate concentrations of colloids, RMSA is sufficient to predict , and as shown in Figures 1(b), 2, 4. Indeed Figure 7 indicates that MSA theory for the structure factor S(k) of a very complex ferrofluid made of polymeric solvent leads to an excellent quantitative prediction of up to hydrodynamic volume fraction of
Point 8: The colloidal ferrofluids physical properties must be included in the study.
Response 8: All ferrofluids' physical properties appear now in lines 116 to 143.
From lines 204 to 208, from lines 222 to 227, from lines 250 to 253, and from lines 263 to 267
Point 9: The proposed stochastic approach for the study must be described.
Response 9: The stochastic approach used in this manuscript is fully described now in Appendix A, line 334
Point 10: Please clarify the application of this investigation.
Response 10: In the introduction section, and line 22 we state the application of this investigation. It is contained in the paragraph “Nowadays, the experimental study of rheology in well-characterized ferrofluids is amply documented, either in the presence or absence of external magnetic fields [1]. Ferrofluids consist of nanometer-size magnetic particles dispersed in a solvent. Nonetheless, modeling the viscosity and transport properties as the self-diffusion of the magnetic particles has not reached the same level of understanding. Yet the measurement of the diffusion coefficient at diverse thermodynamic conditions of solvent properties, colloid volume fraction, and dipolar strength is not known. With this motivation, this manuscript proposes a stochastic model to determine the self-diffusion and viscosity of monodisperse ferrofluids. These transport properties rely upon the accurate knowledge of the microstructure of the ferrofluid given by the structure factor. According to our understanding, scarce publications in the literature on a comprehensive experimental study of the microstructure and its relation to the dynamics in the same well-characterized magnetic fluid are noticeable. This manuscript aims to contribute to developing a first principle approach to understanding the rheology of ferrofluids.”
Point 11: Figure caption is missing in all the plots, this must be presented
Response 11: All figure captions have already been corrected.
Point 12: In Figure 1 discussion, the referred and cited articles are not appropriately presented. The
Authors names and their initial are specified, which is not in line with other cited articles.
Response 12: Caption of figure 1 is now corrected with appropriate citation of previous work by other Authors
Point 13: For a scientific report, the uses of pronoun are not encouraged, as such, all cases of ‘’we, he,
she, I, etc.’’ should be removed.
Response 13: The use of pronouns was now eliminated in the new version of the manuscript
Point 14: Some grammatical mistakes should be checked through.
Response 14: In this new version of the manuscript, grammatical mistakes have been reduced to a minimum,
Point 15: All figures should be discussed from the physical implications, significance justification
Point of view, hence, the discussion of results section needs to be improved.
Response 15: The Results and discussion section was modified entirely for this purpose
Point 16: Why has the author chosen to engage in this study?
Response 16: In the Abstract and Introduction section, we introduce an overview of the open problems of both experimental and theoretical modeling of rheology in ferrofluids. Particularly, our
Manuscript point out the necessity to develop comprehensive studies of the microstructure
through scattering sources, which presently have the shortcoming of low wave vector resolution.
It was also exemplified the disconnection between that microstructural knowledge from the
dynamical properties studies on the same well-characterized ferrofluid systems. It is expected
the present manuscript will help motivate and contribute to fulfilling these apparent gaps in fundamental knowledge of ferrofluid material properties from a well-sounded statistical mechanical theory.
Point 17: Likely extension of the study should be stated or recommended.
Response 17: In the conclusion section, new feasible extensions of this theoretical approach are proposed, which is research work underway and its comparison with existing experimental data.
Point 18: The conclusion of the study is very weak, expansion needed.
Response 18: To answer this point, the conclusion section was expanded to adequately describe this manuscript's results.
Point 19: 90% of the references are very old, this is not good for a state of the earth research work. As
such, more recent related articles should be cited to improve the quality of the work.
Response 19: In this new manuscript version, five references were eliminated since they are redundant and their main contents appear in the twelve remaining references cited. However, it should be noticed that references [8,9,10, 11] are from the 80’s decade and refers to a fundamental sound knowledge of physics and statistical mechanics methods proved in the past that yield a solid base to construct new models. Thus, they are considered a solid starting base to develop new approaches to colloid dynamics and their structural properties.
Point 20: The study presented is not explicit, comprehensive and may not attracted readers.
Response 20: The new version introduces a major revision of the manuscript according to the observations made by the reviewers.
Point 21: Many facts are missing from the write-up, which make the study not too interesting
Response 21: Since the manuscript experienced a significant revision, it now includes many details on the physical properties and conditions of the ferrofluids studied. Also, Appendices A., B, and C add more information on the numerical procedure to apply the RMSA theory, and the stochastic method of the diffusion and rheology of the ferrofluid for the reader can reproduce all results of this manuscript.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments for author File: Comments.pdf
Author Response
Response to Reviewer 2 Comments
Thank you very much for your valuable comments regarding our manuscript.
In this letter, we would like to explain our revisions.
Point 1: From the abstract, i cannot understand what the research is all about the whole abstract
have to restructured
Response 1: The whole manuscript had significant revisions to answer this point. Consequently
the Abstract section was rewritten too in this new version of the manuscript.
Point 2: In the first paragraph of the abstract the general introduction has to be illustrated
follow by the problem statement, the main aim, the methodology approach and the
results. This format was not followed.
Response 2: The abstract now include this format. It appears: “ One primary concern in colloid science is understanding the relationship of its macroscopic rheology and diffusion behavior with the observed microscopic arrangements of the nanoparticles in the fluid. This manuscript addresses the study of these dynamical properties through a first principle stochastic method. Both properties directly relate to the observed fluid structure factor, which depends on a few known material parameters. However, in the literature, this static quantity is reported up to the first prominent peak of its small momentum transfer of the scattered radiation leading to inaccurate determination of the transport properties. Here it is proposed to use the rescaled mean spherical approximation under the requirement to fit the experimental data of the structure beyond more significant wave numbers dependence. The predicted viscosity agrees with the observed ones at a low volume fraction of particles for ferrofluids dispersed in polymer solvents. This rheological quantity is inversely related to the self-diffusion coefficient of a tracer particle.
” which answers this point more appropriately.
Point 3: In research work all the keywords have to be in the abstract section before you can
state them has the keywords. I did not understand where you brought all this keywords
you stated in the manuscript.
Response 3: According to this point, the keywords are first mentioned in the Abstract, followed by their statement: ” Keywords: rheology; self-diffusion; viscosity; ferrofluid, structure factor.”
The keywords: microrheology, colloidal magnetic fluid, and viscoelasticity, which did not appear in the previous version of the manuscript, were eliminated, and the new keyword: structure factor
was added
Point 4: The introduction part is not constructive, kindly add more information from different
kinds of literature
Response 4: The Introduction section was rewritten entirely in this new manuscript to answer this point. All content of the Materials and Methods section of the previous version of the manuscript was moved to the new Introduction section. Including the literature cited within. The reference [1] Odenbach, S. Ferrofluids: Magnetically controllable fluids and Their Applications 2nd. Ed.; Berlin, Germany, 2002: pp 1-253. was added. This is a comprehensive updated literature review from experimental studies and models of transport properties in ferrofluids. We eliminated five references which content is covered by the twelve cited references that appear in this new manuscript version.
Point 5: “We applied the rescaled mean spherical approximation to these magnetic fluids as a
theoretical method to reproduce the experimentally observed microstructure of the
ferrofluids” reconstruct this this sentence in a scientific manner
Response 5: This phrase appeared in lines 39 to 32 in the Introduction section of the previous version of the manuscript. The new Introduction changed it. Since this point is related to the other reviewers' observations, it was entirely rephrased as “ Nowadays, the experimental study of rheology in well-characterized ferrofluids is amply documented, either in the presence or absence of external magnetic fields [1]. Ferrofluids consist of nanometer-size magnetic particles dispersed in a solvent. Nonetheless, modeling the viscosity and transport properties as the self-diffusion of the magnetic particles has not reached the same level of understanding. Yet the measurement of the diffusion coefficient at diverse thermodynamic conditions of solvent properties, colloid volume fraction, and dipolar strength is not known. With this motivation, this manuscript proposes a stochastic model to determine the self-diffusion and viscosity of monodisperse ferrofluids. These transport properties rely upon the accurate knowledge of the microstructure of the ferrofluid given by the structure factor. According to our understanding, scarce publications in the literature on a comprehensive experimental study of the microstructure and its relation to the dynamics in the same well-characterized magnetic fluid are noticeable. This manuscript aims to contribute to developing a first principle approach to understanding the rheology of ferrofluids.
Therefore, a proposed dynamical model will be helpful if it is based on comprehensive experimental data of the fluid-structure and contrasted with their observed dynamics. Scattering techniques of neutrons, small angle X-rays, and forced Raleigh experiments yield access to the structure factor of ferrofluids [2,3,4]. A significant drawback of this observed static property is its limited short momentum transfer dependence due to the limited resolutions of the scattering radiation techniques to its larger magnitudes. They only provide the prominent structure factor peak in the low wave vector regime and neglect its tail, which contains non-negligible spatial information.
For this reason, this manuscript resorts to one of the most numerically economical methods, yet accurate enough to determine the structure factor of the colloid. This manuscript uses a rescaled mean spherical approximation fit of known experimental structure factors to accurately assess their total wave number contributions. As a result, the present study renders a novel prediction of diffusion and viscosity of the ferrofluid without arbitrarily adjustable parameters. It depends solely on materials data of volume fraction of particles and dipole strength associated with the structure factor. Thus, a comparison of this model for the viscosity of ferrofluids dispersed in polymer solutions shows their agreement at a low volume fraction of particles and deviates at higher concentrations. Previous studies on such rheology properties use a thermodynamically motivated fixing parameter to explain the same experimental data [1,5]. Appendix A introduces the stochastic method used in this manuscript. Its principal physical results are summarized as follows. During its diffusion, a tracer colloidal particle experiences interaction with the cloud of others surrounding it, contributing to a friction ∆ζ. Additionally, the hydrodynamic friction contributes to the slowing down of its motion due to the solvent (sol) with a viscosity also depends on the concentration of the other particles at the volume fraction . That is to say, gives the total friction on the tracer particle. References [6,7] demonstrated that the diffusion coefficient of the tracer particle at the longtime (so-called overdamped diffusion regime) satisfies a Stokes-Einstein relationship , whose explicit form is
|
(1) |
|
|
|
|
where and he second term in the square bracket on the right-hand side of (1) is . is the Boltzmann constant, and is the absolute temperature. Notice that equation (1) is given precisely in terms of the structure factor , which presently is an unknown quantity to the theory of Eq. (1). The present manuscript does not concern the measurement of the structure factor. However, an independent study appears reported in References [2,3,4] for several magnetic colloids. The main difficulty is its insufficient and limited wave number measurement associated with the experimental techniques. The following section describes how to extend it to larger through the so-called rescaled mean spherical approximation (RMSA) by a fit of those experimental of [2,3,4]. In Eq. (1), the short-time friction considers the hydrodynamic interaction among the magnetic particles, which is vital for concentrated colloids. This property has not been measured for ferrofluids yet. Therefore, this manuscript resorts to its experimental counterpart corresponding to an equivalent hard sphere colloidal suspension of polystyrene particles given in Ref. [8] without electrical charge. The Carnahan-Starling pair correlation function also gives its approximated theoretical value [9]. For a very low concentrated suspension acquires its Stokes form of a free diffusing particle. Where is the particle diameter, , and is the number density for a colloid constituted by colloidal particles occupying a sample volume . References [6,7] showed that the total tracer friction has a linear relationship with the static viscosity of ferrofluids and has the simple expression
|
(2) |
In equation (2), due to the hydrodynamic interactions (HI) among all the particles, the normalized self-diffusion coefficient includes the modification of the Stokes free particle friction .
Because of the diffusion, Eq. (1) and viscosity (2) shows a dependency on which enters as an external input to this theory. A route to its knowledge is given by the analytical rescaled mean spherical approximation (RMSA) of the structure factor of hard spheres introduced by Hayter and Penfold [10]. Hansen and Hayter [11] demonstrated that it could accurately reproduce the experimental stricture factor of a fluid made of particles with Yukawa repulsive interaction. This method rescales with a parameter the wave number , volume fraction η’, ionic electrolyte strength κ,’ and diameter of the particle the parameters of the original system; , , , , to preserve the analytical mean spherical approximation of Hayter and Penfold [11] for the structure factor with
(3)
which describes a colloidal dispersion of particles with repulsive pair interaction energy in electrolytes
|
(4) |
where and . The factors A, B, C, and F, have involved expressions whose definitions are in Ref. [11].
”
Point 6: For the validation of your approach one viscosity experiments have to be perform
from your lab and compare with the other works, since your work is not a review
paper
Response 6: We would like to inform you that presently we do not have a laboratory or experimental set up to perform measurements of the structure factor or viscosity of ferrofluids, However, as we point out in the conclusion section, the predictions of our model of viscosity based on existing data of real ferrofluid, may motivate the corresponding practical verification in the future
either by other research groups or us.
Author Response File: Author Response.pdf
Reviewer 3 Report
Title: The viscosity and self-diffusion of some real colloidal ferroflulids
Manuscript ID: colloids-1924652
Authors: Avalos-Gonzalez et al.
Dear Authors,
Thank you for the opportunity to read your article. I found the topic is interesting and fundamental. Generally speaking, there are some results presented in order to capture some trends but the methods and results need more clear explanation and detail discussion with fair point of view. I suggest that this article will be revised extensively before its re-submission for another review process if applicable. As a conclusion, I recommend its major revision/rejection at this state.
I hope my comments are helpful.
Good luck,
A reviewer
Major concerns:
“Abstract”
->Please consider revising the abstract by following the journal guideline (https://www.mdpi.com/journal/colloids/instructions).
1) Background: Place the question addressed in a broad context and highlight the purpose of the study; 2) Methods: Describe briefly the main methods or treatments applied. Include any relevant preregistration numbers, and species and strains of any animals used. 3) Results: Summarize the article's main findings; and 4) Conclusion: Indicate the main conclusions or interpretations.
“Keywords”
->Please consider providing keywords that are not used in the article title.
“1. Introduction”
-Introduction is too general and not directly relevant to your specific study. Please consider focusing on the topics directly relevant to your study.
-Based on your literature review, in the introduction, please consider clearly stating research gap(s) you tried to address in this study. In other words, please mention why you studied “the tracer diffusion and rheology of the magnetic fluid....”
-In the introduction, please also consider mentioning the originality of your work.
“2. Materials and Methods”
-In this section, please consider introducing the physical properties and conditions of “Ferro-particle” and “ferrofluids” you studied. (*, see the other comment on results and discussion)
-Please keep the technical words consistent throughout the article. For example, is “the tracer particle” same as “the labeled particle”?
-Lines 52-53: “…the experimentally observed structure factor S(x)…”->In this section, please consider mentioning how you perform the experiment and determine S(x). (*, see the other comment on results and discussion)
-In this section, please consider keeping the contents directly relevant to your study and clearly mentioning what you actually did, and sending the literature review contents to the introduction. In the current status, it seems that you simply introduce literature but a reader will not understand what you actually did in your study.
“3. Results and Discussion”
-In general, the results are simply described but not discussed. Please consider discussing your results more in detail and a fair point of view, and comparing with literature. You can see some of my comments below for this purpose. In addition, the originality of your work can be clearly written if there is any.
-Figure 1(a) (and elsewhere): RMSA model does not fit experimental data well depending on the conditions. Please consider assigning error bars on the resultant self-diffusion coefficient and viscosity in Figure 1(b) (and elsewhere). In addition, you have only 2 datasets for ϕ = 0.155 and 0.07 while you have 7 results of D/D0. Please consider mentioning how you generated those results. Did you actually have 7 datasets with different ϕ ?
-Figure 3: “The same thermodynamic properties…”->Please consider revising the figure title as it is very confusing. What you did was that you used the different structure factor data sets to fit with RMSA model to determine D/D0 and η/ηsol?
-Please consider sending materials and conditions information to Materials and Methods section (*, see the other comment on materials and methods).
-Lines 201-206: The contents described here are literature review. Please clearly mentioning their correlation with your results.
“5. Conclusion”-> 4. Conclusions?
-Lines 209-210: “…its direct determination of ferrofluids.”->Please be more specific about what you actually reported in this article, i.e. D/D0 and η/ηsol.
-You may state future perspectives in Conclusions.
Minor concerns:
-Please consider polishing English more. You may use some of my comments above for this purpose.
Author Response
Response to Reviewer 3 Comments
Thank you very much for your valuable comments regarding our manuscript.
In this letter, we would like to explain our revisions.
Point 1: Major concerns:
“Abstract”
->Please consider revising the abstract by following the journal guideline (https://www.mdpi.com/journal/colloids/instructions).
1) Background: Place the question addressed in a broad context and highlight the purpose of the study; 2) Methods: Describe briefly the main methods or treatments applied. Include any relevant preregistration numbers, and species and strains of any animals used. 3) Results: Summarize the article's main findings; and 4) Conclusion: Indicate the main conclusions or interpretations.
Response 1: According to this observation, we changed the abstract to include these guidelines. We believe it addresses in its new version all points raised.
“Keywords”
->Please consider providing keywords that are not used in the article title.
Response 1: In the previous manuscript version there were six keywords. Now we eliminated five and added a new one; structure factor. All keywords are mentioned in the abstract and they are: “ Keywords: rheology; self-diffusion; viscosity; ferrofluid, structure factor.”
“1. Introduction”
-Introduction is too general and not directly relevant to your specific study. Please consider focusing on the topics directly relevant to your study.
-Based on your literature review, in the introduction, please consider clearly stating research gap(s) you tried to address in this study. In other words, please mention why you studied “the tracer diffusion and rheology of the magnetic fluid....”
-In the introduction, please also consider mentioning the originality of your work.
Response 1: the introduction section of the manuscript now emphasizes several central gaps that deserve investigation from our point of view. It is argued that there is a complete lack of studies on well-characterized ferrofluids about their microstructure. That follows with corresponding analyses of the importance of such structure on observed rheological behavior. This manuscript intends to contribute to the development of a first principle model to provide a link between these two phenomena. Nowadays, the experimental study of viscosity use models that depend on physicaly motivated fixing parameters that do not have a fundamental justification. They appear as ad hoc temporal assumptions to aid in interpreting the data. These observations were added in the new version of the introduction section and motivated the novelty of our stochastic viscosity method.
“2. Materials and Methods”
-In this section, please consider introducing the physical properties and conditions of “Ferro-particle” and “ferrofluids” you studied. (*, see the other comment on results and discussion)
Response 2: All ferrofluids' physical properties appear now fully described in the following lines:
From 116 to 143.
From lines 204 to 208,
from lines 222 to 227,
from lines 250 to 253,
and from lines 263 to 267
-Please keep the technical words consistent throughout the article. For example, is “the tracer particle” the same as “the labeled particle”?
Response 2: The exact phrase “tracer particle” is now used in the manuscript's main text.
-Lines 52-53: “…the experimentally observed structure factor S(x)…”->In this section, please consider mentioning how you perform the experiment and determine S(x). (*, see the other comment on results and discussion)
Response 2: To answer this point we added in the lines from 68 to 75 the following phrase to make clear that this manuscript is not concerned with the measurement of the static structure S(x) of the ferrofluid; “…temperature. Notice that equation (1) is given precisely in terms of the structure factor , which presently is an unknown quantity to the theory of Eq. (1). The present manuscript does not concern the measurement of the structure factor. However, an independent study appears reported in References [2,3,4] for several magnetic colloids. The main difficulty is its insufficient and limited wave number measurement associated with the experimental techniques. The following section describes how to extend it to larger through the so-called rescaled mean spherical approximation (RMSA) by a fit of those experimental of [2,3,4]. … ”
-In this section, please consider keeping the contents directly relevant to your study and clearly mentioning what you actually did, and sending the literature review contents to the introduction. In the current status, it seems that you simply introduce literature but a reader will not understand what you actually did in your study.
Response 2: Following these observations, we modified the section Materials and Methods to explain what was done in this manuscript.
“3. Results and Discussion”
-In general, the results are simply described but not discussed. Please consider discussing your results more in detail and a fair point of view, and comparing with literature. You can see some of my comments below for this purpose. In addition, the originality of your work can be clearly written if there is any.
Response 3: This section was rewritten to discuss the shortcomings of the stochastic model and how the errors of the structure factor on which it depends as critical information modify its predictions on the viscosity of ferrofluids. In this section, we discuss the usefulness of the proposed viscosity model to correctly fit the experimental data on a complex ferrofluid in polymer solvents (See Figure 7) at a low hydrodynamic volume fraction, using a repulsive interaction between the particles solely. Such a comparison abounds in its originality. For this purpose, we added de new reference [5];
Balau O.; Bica, D.; Koneracka, M.; Kopcansky, P.; Susan-Resiga, D.; Vekas, L. Rheological and magnetorheological behaviour of some magnetic fluids on polar and nonpolar carrier liquids. Int. J. Mod. Phys. B 2002, 16, 2765-2771.
And we eliminated five references whose content is covered by the remaining twelve references.
-Figure 1(a) (and elsewhere): RMSA model does not fit experimental data well depending on the conditions. Please consider assigning error bars on the resultant self-diffusion coefficient and viscosity in Figure 1(b) (and elsewhere).
Response 3: We added error bars now. They are the same size as the symbols used for the self-diffusion coefficient and viscosity. In lines 175 to 181, there is a phrase that explains how standard error was determined: “ … interactions. Standard errors bars of and are on the order and they appear in Fig. 1(b). The errors result from recalculating each plotted value of and in Figure 1(b) at the five lower values of for each of the seven ϕ in steps . For each of the five , the initial condition on the numerical difference of the fitted versus the experimental one was the minimum in each of the five cases, which requires the additional boundary condition on the radial distribution function at the rescaled diameter , (see Appendix B). ...”
In addition, you have only 2 datasets for ϕ = 0.155 and 0.07 while you have 7 results of D/D0. Please consider mentioning how you generated those results. Did you actually have 7 datasets with different ϕ ?
Response 3: This point is replyed in the previous response.
-Figure 3: “The same thermodynamic properties…”->Please consider revising the figure title as it is very confusing. What you did was that you used the different structure factor data sets to fit with RMSA model to determine D/D0 and η/ηsol?
Response 3: The previous figure 3 in the old version of the manuscript was split into new ones, new figures 3 and 4.
New figure 3 contains additional information previously not included in it because of reply to the query “3. Results and Discussion” above, … and comparing with literature. …” Where we compare our RMSA theory fit to experimental S(k) with the same type of calculations made
By the different groups Wagner et al., as explained in the caption of this figure. For clarity of resolution of Figure 3, it was made a separate figure 4 that contains the prediction on self-diffusion
And viscosity of the ferrofluid in figure 3. The explanation on how to determine self-diffusion and viscosity at seven new volume fractions is explained in lines 161 to 167 with the phrase:
“… (0.119101, 0.781029). On the other hand, the RMSA fitting of for ϕ = 0.07 implies that there is a mapping of the factors , A, B, C, and F onto the potential energy Eq. (4) with rescaled amplitude of interaction and dimensionless rescaled screening length This fact permits studying model systems derived from the actual colloidal suspension by varying only the volume fractions. Each of the above seven volume fractions , corresponds to a different rescaled one given by that lead to the new structure factor through Eq. (3). …”
-Please consider sending materials and conditions information to Materials and Methods section (*, see the other comment on materials and methods).
Response 3: This was done in the new manuscript version
-Lines 201-206: The contents described here are literature review. Please clearly mentioning their correlation with your results.
Response 3: This correlation is explained in the lines 314 to 319 with the new phrase “… ferrofluids through the use of the structure factor of the colloid. For the viscosity, its practical measure may use the dissipative modulus of the colloid at longtime (equivalently short frequencies) [6]
|
(5) |
where the frequency is roughly the inverse of the diffusive relaxation time of the particles. We point out that Eq. (5) yields a way to know such a transport property, namely or . …”
“5. Conclusion”-> 4. Conclusions?
-Lines 209-210: “…its direct determination of ferrofluids.”->Please be more specific about what you actually reported in this article, i.e. D/D0 and η/ηsol.
-You may state future perspectives in Conclusions.
Response 5: We modified completely the conclusion section to make clear what was done in this manuscript. The new conclusion paragraph reads:
“ The results depicted in figures 1(a), two, and four present a new method to study the tracer particle self-diffusion and viscosity in thermally equilibrated ferrofluids without external magnetic fields. These transport properties depend critically on the accurate determination of the fluid's structure factor ?(?). For known maghemite ferrofluids in aqueous citrate elecytrolytes, Figure 1(a) shows its fitting with the help of RMSA liquid theory and provides its whole wave vector resolution. RMSA performance is better for low volume fractions ϕ = 0.07 of particles and deteriorates for higher concentrations. Using the best-fitted ?(?) at ϕ = 0.07 allows the underlying potential between particles given by Eq. (4). Therefore, equations (1) and (2), which are expressed in terms of ?(?), consequently the potential, render a first principle link with the microscopic origin of the particle diffusion and viscosity of the ferrofluid. This approach yields a new method for studying viscosity in ferrofluids. For the colloid at concentration ϕ = 0.07 Eqs. (1-2) demonstrated in Figure 2 its practical application to predict the rheology of this system. Figures 3 and 4 for cobalt ferrite nanoparticles illustrate a second realization of the proposed stochastic methods of Eqs. (1-2) to describe the rheology of another interesting aqueous magnetic fluid. Yet the self-diffusion and viscosity predictions in Tables 1 and 2 of a maghemite ferrofluid in citrate aqueous electrolyte may motivate its experimental confirmation in the future. This conclusion resides in Figure 7, which demonstrates that the viscosity model can successfully explain experimental data for low hydrodynamic volume fraction of complex ferrofluids with polymer solvents with minimum structural information. Possible extension of this approach includes polydisperse ferrofluids effects and the presence of external electric and magnetic fields.
”
Minor concerns:
-Please consider polishing English more. You may use some of my comments above for this purpose
Response : We reduced the wording mistakes to the minimum
Round 2
Reviewer 1 Report
The manuscript is improved, it can be accepted for possible publication
Reviewer 2 Report
The authors have addressed all the questions raised, the manuscript can be accepted for publication.
Reviewer 3 Report
Dear Authors,
As all the comments were addressed, I would suggest the journal accept this article for its publication.
Best regards,
A reviewer
